Joint full wavefield inversion of P-wave velocity and attenuation using an efficient first order optimization

1. A method for iteratively inverting seismic data to jointly infer a model for at least P-wave velocity and attenuation parameters of the subsurface, said method comprising:

jointly inverting the P-wave velocity and attenuation parameters with an iterative visco-acoustic full wavefield inversion process, wherein the iterative visco-acoustic full wavefield inversion process includes computing a gradient of an objective function, the objective function measuring a misfit between all or part of the seismic data and corresponding model-simulated seismic data;

for each of the P-wave velocity and attenuation parameters, computing a search direction in model space from the gradient;

determining line search step sizes α and β for the search directions for the P-wave velocity and attenuation parameters, respectively, wherein a ratio of the step sizes is a function of the P-wave velocity parameter; and

using the step sizes α and β and the search directions for each of the P-wave velocity and attenuation parameters, computing a new search direction in model space, then performing a line search along the new search direction to arrive at a new step size, and using the new step size and the new search direction to generate an updated model for a current iteration of the iterative visco-acoustic full wavefield inversion process;

wherein the step sizes satisfy

β

α

≈

-

π

V

p

⁢

log

⁡

(

ω

ω

0

)

,

V p is the P-wave velocity parameter, ω is frequency and ω o is a reference frequency.

2. The method of claim 1 , wherein the obtaining the starting P-wave velocity model includes determining, with a computer, the starting P-wave velocity model from an iterative acoustic full wavefield inversion process, wherein the iterative acoustic full wavefield inversion process includes using a cross-correlation objective function to minimize a misfit between all or part of the seismic data and corresponding model-simulated seismic data.

3. The method of claim 1 , wherein the objective function is an L2 objective function.

4. The method of claim 1 , wherein the objective function is a cross-correlation objective function.

5. The method of claim 1 , further comprising:

generating a subsurface image from the updated model; and

using the subsurface image to prospect for hydrocarbons.